Spring 08
Mathematics 506C: Research on the Teaching of Mathematics
Tuesdays 5:30 – 8:00 PM
Math East 141
Marta Civil Virginia Horak Leslie Kahn
civil@math.arizona.edu horak@math.arizona.edu lkahn@math.arizona.edu
Math 203 Math 522 Math East 243
621-6873 626-5287 626-9393
The topic for this course is research on the teaching of mathematics. In particular, we will focus on aspects of Teacher Knowledge, Teacher Beliefs, and Learning to Teach. We will examine these aspects both in preservice and inservice teacher education, as well as from national and international perspectives. The course will include issues related to teaching various content in mathematics
There is no required text for the course; there will several readings handed out during the semester.
Required Course Website:
d2l.arizona.edu (website will be used to post required readings, assignment guidelines, and to submit all course assignments)
The course will be run like a seminar with a pair of students each week facilitating the discussion of the articles. Class sessions will include short lectures, small-group conversations, whole-class discussions of readings, and in-class activities. To ensure the flavor of a seminar, studentsŐ participation is crucial. A major part of this course is reading and discussing ideas/issues related to teaching and learning mathematics as they relate to the readings; therefore adequate time spent preparing for each class period is expected of every student – read assigned material thoroughly and take some notes as you read. Attendance is mandatory. Please be aware that excessive or unexcused absences will result in significantly lowering your grade, and/or dropping you from the class.
Academic dishonesty will not be tolerated under any circumstances, and will result in a failure to pass this course. Misrepresenting the words or ideas of another as your own is called plagiarism. The key to avoiding plagiarism is to develop good judgment in the fair attribution of words and ideas. You must credit the source whenever you (a) directly quote the words of another or (b) reference a specific idea, argument, or fact from a given source. You should err on the side of caution and cite the source of any specific ideas (such as lesson plan ideas), concepts, or facts that you might use in a paper.
The University of Arizona seeks to provide reasonable accommodations for all qualified individuals with disabilities. If you anticipate issues related to the format or requirements of this course, please meet with me. I would like us to discuss ways to ensure your full participation in the course. If you determine that formal, disability-related accommodations are necessary, it is very important that you be registered with Disability Resources (621-3268; drc.arizona.edu) and notify the instructors of your eligibility for reasonable accommodations. We can then plan how to coordinate your accommodations.
Activities
There will be four main ŇactivitiesÓ in this course:
In-class work: as discussion facilitators you will be expected to prepare some questions and / or activities related to the readings assigned for your session, and post these questions on d2l by Wednesday prior to your day of facilitating the session. As a participant, your responsibility will be to have carefully read the articles, and come to class prepared to discuss the questions.
PROJECT I (in groups but individual write-up): Task-based interview to assess Preservice Elementary TeachersŐ understanding of fractions.
In small groups (2 or 3) you will come up with a series of tasks to assess fraction concepts. We will also discuss these tasks as a whole class; then each small group will end up with a task-based interview with 3 or 4 tasks that each of you will use to individually interview a preservice elementary teacher (or a pair of students if this is more comfortable for the preservice teachers) currently enrolled in Math 302B (the topic of fractions is covered in Math302A). You will each write a short report (3 to 5 pages) on the findings of your interview, including a reflection on the experience of interviewing.
Deadlines:
a) In-class presentation of the findings from the interviews. This will be a group presentation, that is, each group will put together a powerpoint presentation that combines the findings from the different interviews.
b) Individual paper (3 to 5 pages) reporting on each studentŐs interview is due.
PROJECT II (can be done in pairs): Small case study on a practicing teacher
We will give you access to experienced teachers who have agreed to help out in this project (or if you know a teacher who is willing to help you out, feel free to work with him/her). Your work with each teacher will start the same way for each of you with a short interview to gather some background information as well as a small profile of their beliefs about teaching mathematics (with a focus on teaching and diversity). For that first interview, you will use a common instrument that we will distribute in class. Then, the rest of the project is your choice: you need to select a topic of interest that you want to explore further. For example, you may want to investigate this teacherŐs use of questions and/or tasks in his / her teaching of mathematics; or issues related to the participation of students in classroom discussions; or the teaching of a specific topic; or a topic related to language and mathematics;
Your case study will involve 3 or 4 classroom observations and 1 or 2 interviews / conversations with the teacher (in addition to the initial one). There will be a Poster presentation of your case study on the last day of class (May 6)
Deadlines:
b) Case study (paper) due
Guidelines for paper:
Your 10 to 14 pages paper should have the following sections:
PROJECT III (individual): Brief review of the literature
You will select a topic related to the theme of the course (research on the teaching of mathematics). Your topic may be an elaboration of a topic we discussed in the course or it may address a different topic (as long as it relates clearly to the overall theme of the course). Example of topics are: teacher content knowledge in mathematics, teacher beliefs, a form of professional development, equity and teacher education, teaching a specific topic, research on questioning or tasks (e.g. cognitive demand, etc.).
For your review of the literature you are expected to read and discuss 6 or 7 research articles; you can include readings we have discussed in class, but those will not count towards the 6 or 7 articles. Your 10 to 14 pages paper should include a final section on implications for further research based on your interpretation of the articles you read.
Deadlines:
Format for Papers
APA style (fifth edition) is required for all write-ups. All write-ups should be double-spaced with 1 inch margins on all sides. Block quotes should be single-spaced and indented. Use a 12-point font and a standard font style (i.e., CG Times, Arial, or Times New Roman).
Tentative Schedule
(We may change some readings as the course progresses)
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Day: |
Topic: |
Activity / Readings (due on date indicated on far left column): |
Assignments: |
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Jan 22 |
Course Overview
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á An overview of research in mathematics teacher education: o Adler, J., Ball, D., Krainer, K., Lin,F-L, & Novotna, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. ESM, 60, 359-381. o Lerman, S. (2001). A review of research perspectives on mathematics teacher education. In F-L Lin & T. Cooney (Eds.), Making sense of mathematics teacher education (pp. 33-52). Boston, MA: Kluwer. á Preparing for Project I: Fractions á Fractions in Math302A (Laura)
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Jan 29
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Course Overview |
á Sowder, J. (2007). The mathematical education and development of teachers [2nd handbook of research on mathematics teaching and learning] á Work on tasks for the fraction interview |
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Feb 5 |
Research on Teacher Professional Development: Study Groups and Lesson Study |
á Crespo, S. (2006). Elementary teacher talk in mathematics study groups. ESM, 63,29-56. á Arbaugh, F. (2003). Study groups as a form of professional development for secondary mathematics teachers. JMTE, 6, 139-163 á Fernandez, C. (2005). Lesson study: A means for elementary teachers to develop knowledge of mathematics needed for reform-minded teaching? MTL,7, 265-289. |
Task-based interview protocol due [Project I] |
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Feb 12 |
Professional Development: Guest presentation |
á Deborah Schifter á [Readings TBA] |
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Feb 19 |
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á Working time (Projects I and II) |
Interview 1 for Project II should be done |
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Feb 26 |
Research on teachersŐ beliefs |
á Philipp, R. (2007). Mathematics teachersŐ beliefs and affect. [2nd handbook of research on mathematics teaching and learning] á Gates, P. (2006). Going beyond belief systems: Exploring a model for the social influence on mathematics teacher beliefs. ESM, 63, 347-369. |
Proposal for case study for Project II is due |
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March 4 |
Research on teachersŐ knowledge
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á Hill, Sleep, Lewis, & Ball (2007). Assessing teachersŐ mathematical knowledge: What knowledge matters and what evidence counts? [2nd handbook of research on mathematics teaching and learning] á Adler, J. & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. JRME, 37, 270-296. |
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March 11
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á Project I reports (small group powerpoints) á Time to work on Project II |
Project I – write up due |
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March 18 |
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SPRING BREAK |
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March 25 |
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AERA [Working Session – No formal class meeting] |
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April 1 |
Theory-Practice |
á Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice [2nd handbook of research on mathematics teaching and learning] á Scherer, P. & Steinbring, H. (2006). Noticing childrenŐs learning processes-teachers jointly reflect on their own classroom interaction for improving mathematics teaching. JMTE, 9, 157-185 |
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April 8 |
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á Progress report on Project II á Time to discuss Project III progress (Review of Literature) |
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April 15 |
Research on Preservice Teacher Education |
á Garc’a, M., S‡nchez, V., Escudero, I., & Llinares, S. (2006). The dialectic relationship between research and practice in mathematics teacher education. JMTE, 9, 109-128. á Lloyd, G. (2006). Preservice teachersŐ stories of mathematics classrooms: Explorations of practice through fictional accounts. ESM, 63, 57-87. |
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April 22 |
Research on Teacher education and diversity |
á Vithal, R. (2003). Teachers and Ôstreet childrenŐ: On becoming a teacher of mathematics. JMTE, 6, 165-183. á Khisty, L. L. (2001). Effective teachers of second language learners in mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th international group for PME, (vol. 3, 225-232). Utrecht, The Netherlands: Freudenthal Institute. á GutiŽrrez, R. (2002). Beyond essentialism: The complexity of language in teaching mathematics to Latina/o students. AERJ, 39, 1047-1088. |
Project III: outline / draft (optional) |
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April 29 |
Teaching mathematics: An international perspective |
á Cedillo, T. (2006). Learning from students: A study with in-service middle school mathematics teachers in Mexico. PME-NA Proceedings, MŽrida, MX. á Ma, L. (1999). Exploring new knowledge: The relationship between perimeter and area. Chapter 4 in Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence Erlbaum. á Stigler, J. W. & Hiebert, J. (1999). Selcctions from The Teaching Gap. New York, NY: The Free Press. á Santagata, R. & Barbieri, A. (2005). Mathematics teaching in Italy: A cross-cultural video analysis. MTL, 7(4), 291-312 |
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May 6 |
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Poster Presentations on Project II |
Paper for Project II due |
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May 13 |
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Final Exam |
Review of Literature (Project III) due |
Resources
JOURNAL LIST
Educational Studies in Mathematics (ESM) - http://www.springerlink.com/content/1573-0816/
Focus on Learning Problems in Mathematics (FLPM)
For the learning of Mathematics (FLM) - http://flm.educ.ualberta.ca/
Journal for Research in Mathematics Education (JRME) –
http://my.nctm.org/eresources/journal_home.asp?journal_id=1
Journal of Mathematical Behavior [JMB] –
http://www.elsevier.com/wps/find/journaldescription.cws_home/620200/description#description
Journal of Mathematics Teacher Education [JMTE] - http://springerlink.metapress.com/content/1573-1820/
Mathematical Thinking and Learning (MTL) (ItŐs published by Lawrence Erlbaum; http://www.erlbaum.com
Mathematics Educator [ME] - http://math.coe.uga.edu/tme/tmeonline.html
International Journal of Mathematics and Science Education [IJMSE] - http://www.springerlink.com/content/111141/?p=d6da58f98d3b4b958773664bc93605bc&pi=0
If you find other journals that have articles relevant to this course please let us know. Here we have listed the most ŇstandardÓ journals in the field.
References (includes the readings for the course and additional resources you may want to check for your papers)
Adler, J., Ball, D., Krainer, K., Lin,F-L, & Novotna, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. Educational Studies in Mathematics, 60, 359-381.
Adler, J. & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education. 37(4), 270-296.
Arbaugh, F. (2003). Study groups as a form of professional development for secondary mathematics teachers. Journal of Mathematics Teacher Education, 6, 139-163.
Ball, D. & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (ed.), Multiple Perspectives on Mathematics Teaching and Learning, 83-104. Westport, CT: Ablex Publishing.
Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachersŐ mathematical knowledge. In V. Richardson (Ed.) Handbook of Research on Teaching.433-456. Washington, D.C.: AERA.
Cai, J. (2005). U.S. and Chinese teachersŐ constructing, knowing, and evaluating representations to teach mathematics. Mathematical Thinking and Learning, 7(2), 135-169.
Cedillo, T. (2006). Learning from students: A study with in-service middle school mathematics teachers in Mexico In S. Alatorre, J.L. Cortina, M. S‡iz, & A. MŽndez (Eds.), Proceedings of the Twenty Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, 51-67). MŽrida, Mexico: Universidad Pedag—gica Nacional.
Comiti, C., & Ball, D. (1996). Preparing teachers to teach mathematics: A comparative perspective. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 1123-1153). Boston, MA: Kluwer.
Crawford, K., & Adler, J. (1996). Teachers as researchers in mathematics education. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 1187-1205). Boston, MA: Kluwer.
Crespo, S. (2006). Elementary teacher talk in the mathematics study groups. Educational Studies in Mathematics, 63, 29-56.
Even, R., & Tirosh, D. (2002). Teacher knowledge and understanding of studentsŐ mathematical learning. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 219-240). Mahwah, NJ: Lawrence Erlbaum
Fennema, E., & Scott Nelson, B. (Eds.) (1997). Mathematics teachers in transition. Mahwah, NJ: Lawrence Erlbaum.
Fernandez, C. (2005). Lesson study: A means for elementary teachers to develop knowledge of mathematics needed for reform-minded teaching? Mathematical Thinking and Learning, 7(4), 265-289.
Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester (Ed.) Second handbook of research on mathematics teaching and learning (pp. 225-256). Charlotte, NC: Information Age Publishing.
Garci‡, M., S‡nchez, V., Escudero, I., & Llinares, S. (2006). The dialectic relationship between research and practice in mathematics teacher education. Journal of Mathematics Teacher Education, 9, 109-128.
Gates, P. (2006). Going beyond belief systems: Exploring a model for the social influence on mathematics teacher beliefs. Educational Studies in Mathematics, 63, 347-369.
GutiŽrrez, R. (2002). Beyond essentialism: The complexity of language in teaching mathematics to Latina/o students. American Educational Research Journal, 39(4), 1047-1088.
Hiebert, J. Morris, A.K. & Glass, B. (2003). Learning to learn to teach: An experiment model for teaching and teacher preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201-222.
Hill, H. C., Sleep, L. Lewis, J. M., & Ball, D. L. (2007). Assessing teachersŐ mathematical knowledge: What knowledge matters and what evidence counts? In F. K. Lester (Ed.) Second handbook of research on mathematics teaching and learning (pp. 111-155). Charlotte, NC: Information Age Publishing.
Jaworski, B., Wood, T., & Dawson, S. (Eds.) (1999). Mathematics teacher education: Critical international perspectives. Philadelphia, PA: Falmer Press.
Kazemi, E. & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203-235.
Khisty, L.L. (2001). Effective teachers of second language learners in mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th international group for PME, (vol. 3, 225-232). Utrecht, The Netherlands: Freudenthal Institute.
Lamon, S. J. (1999). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. Mahwah, NJ: Lawrence Erlbaum.
Lerman, S. (2001). A review of research perspectives on mathematics teacher education. In F.- L. Lin & T. J. Cooney, (Eds.) Making sense of mathematics teacher education (pp.33-52). Boston, MA: Kluwer.
Lin, F.-L., & Cooney, T. (2001). Making sense of mathematics teacher education. Boston, MA: Kluwer
Lloyd, G. (2006). Preservice teachersŐ stories of mathematics classrooms: Explorations of practice through fictional accounts. Educational Studies in Mathematics, 63, 57-87.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.
Peter-Koop, A., Santos-Wagner, V., Breen, C., & Begg, A. (Eds.) (2003). Collaboration in teacher education: Examples from the context of mathematics education. Boston, MA: Kluwer.
Philipp, R. A. ( 2007). Mathematics teachersŐ beliefs and affect. In F. K. Lester (Ed.) Second handbook of research on mathematics teaching and learning (pp. 257-315). Charlotte, NC: Information Age Publishing.
Santagata, R., & Barbieri, A. (2005). Mathematics teaching in Italy: A cross-cultural video analysis. Mathematical Thinking and Learning, 7(4), 291-312.
Scherer, P., & Steinbring, H. (2006). Noticing childrenŐs learning processes-teachers jointly reflect on their own classroom interaction for improving mathematics teaching. Journal of Mathematics Teacher Education, 9, 157-185.
Schifter, D. (Ed.) (1996). WhatŐs happening in math class? Envisioning new practices through teacher initiatives (Vol. 1). New York, NY: Teachers College Press.
Schifter, D. (Ed.) (1996). WhatŐs happening in math class? Reconstructing professional identities (Vol. 2). New York, NY: Teachers College Press.
Sowder, J. T. (2007). The mathematics education and development of teachers. In F. K. Lester (Ed.) Second handbook of research on mathematics teaching and learning (pp. 157-223). Charlotte, NC: Information Age Publishing.
Sowder, J. T., Philipp, R. A., Armstrong, B. E. & Schappelle, B. P. (1998). Middle-Grade teachersŐ mathematical knowledge and its relationship to instruction: A research monograph. Albany, NY: State University of New York Press.
Sowder, J. T., & Schappelle, B. P. (Eds.) (1995). Providing a foundation for teaching mathematics in the middle grades. Albany, NY: SUNY
Stein, M.K., Smith, M.S., Henningsen, M.A., & Silver, E.A. (2000). Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development. New York, NY: Teachers College Press.
Stigler, J. W. & Hiebert, J. (1999). The teaching gap: Best ideas from the worldŐs teachers for improving education in the classroom. New York, NY: The Free Press.
Tirosh, D. (2000). Enhancing prospective teachersŐ knowledge of childrenŐs conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.
Verschaffel, L., Janssens, S., & Janssen, R. (2005). The development of mathematical competence in Flemish preservice elementary school teachers. Teaching and Teacher Education, 21 (1), 49–63.
Vithal, R. (2003). Teachers and Ôstreet childrenŐ: On becoming a teacher of mathematics. Journal of Mathematics Teacher Education, 6, 165-183.
Watson, A., & Geest, E. (2005). Principled teaching for deep progress: Improving mathematical learning beyond methods and materials. Educational Studies in Mathematics, 58, 209-234.